Recently, we posted a video explaining horsepower vs. torque from Engineering Explained’s Jason Fenske. We also posted an article about ARP fasteners and obtaining proper torque. Some of our alert readers noted that in one article we used “pound-feet” exclusively and in the other, the term “foot-pounds” appeared (in the definition of a horsepower). The use of “foot-pound” wasn’t in error, and we’ll explain why.
Are They Interchangeable?
The short answer is no. They are each separate, distinct units of measure. However, as it turns out foot-pound and pound-foot can be converted between one another via complicated math, even though they measure two different things. First, we need to define what each unit is, and what it measures.
The “pound-foot” (lb-ft) is a unit of torque and a vector measurement that is created by one pound of force acting on a one foot lever. The formula for torque in the instance of tightening a fastener would be: Torque equals force times radius, or T=FR. When tightening a bolt, “R” would be the length of your wrench.
The “foot-pound” (or more accurately, “foot-pound-force”), on the other hand, is a measurement of work. Work is the measurement of force over a given distance. So one foot-pound-force (ft-lbf or just ft-lb) is the energy required to move a one pound object one foot of linear distance.
So while both measurements have a force component (pounds) and what is called a displacement component (feet), one is a scalar and one is a vector – which is a fancy way of saying they measure different things.
Which One Is Correct?
No one argues that the correct unit of measure when applying torque to a fastener is the pound-foot. When measuring an engine’s output, however, it seems like anything goes. Since this is the subject of much debate, both online and in real life, we decided to go straight to the automotive authority on engine power measurement – the Society of Automotive Engineers – and get the straight scoop.
The industry standard for measuring an engine’s power output is SAE Standard J1349, which is the standard adopted by SAE to specify a basis for net engine power and torque ratings. “SAE standard J1349, Table 1 lists the units of measure used in the standard as “N-m or lb-ft” for torque and “kW or hp” for the horsepower ratings,” says Gary W. Pollak, P.E., Program Manager for the Society of Automotive Engineers.
The fact that the SAE lists the “pound-foot” as the official unit of measure for engine torque should win you pretty much any argument of semantics you find yourself in. So while that is definitive enough for most folks, that engine output should be correctly referred to in “pound-feet”, we’ve never liked being told “because I said so”, so we won’t do that to you. However, we must warn you: what comes next in this discussion has the potential to hurt your brain.
First, we’re going to look at where the confusion about the units stems from. When Dr. James Watt was looking for a way to equate the ability of a steam engine to the ability of a horse with respect to the same amount of work, he came up with the following definition:
“1 horsepower equals 33,000 foot-pounds of force per minute.” Broken down further, that means that:
The use of “foot-pounds” in the equation is correct (as it was in the article about torque vs. horsepower), yet it is also confusing. If horsepower is “torque over time” as it is often referred, and one horsepower is “550 ft-lbs per second,” that means the “550 ft-lb” is the torque value, right?
Not exactly, and here is why. The basic formula to determine horsepower is as follows:
“To get from pound-feet of torque to horsepower, you need to go through a few conversions. The number 5,252 is the result of lumping several different conversion factors together into one number,” explains Pollak. “Engine speed is normally referred to in revolutions per minute. Since we want a ‘per second,’ we need to convert RPM to ‘something per second’. The seconds are easy – we just divide by 60 to get from minutes to seconds. Now what we need is a dimensionless unit for revolutions: a radian. A radian is actually a ratio of the length of an arc divided by the length of a radius, so the units of length cancel out and you’re left with a dimensionless measure.”
Pollak continues, “You can think of a revolution as a measurement of an angle. One revolution is 360 degrees of a circle. Since the circumference of a circle is (2 times pi times radius), there are 2-pi radians in a revolution. To convert revolutions per minute to radians per second, you multiply RPM by (2-pi/60), which equals 0.10472 radians per second. This gives us the ‘per second’ we need to calculate horsepower.”
Hopefully you’re still with us, because we’re getting into the home stretch. Also, you might be starting to recognize the cancelling of units from the unit analysis method from algebra class. See? Your teachers were right when they told you this would actually apply to the real world.
To get from pound-feet of torque to horsepower, you need to go through a few conversions. The number 5,252 is the result of lumping several different conversion factors together into one number. – Gary W. Pollak, P.E., SAE
“Let’s put this all together. We need to get to horsepower, which is 550 foot-pounds per second, using torque (pound-feet) and engine speed (RPM). If we divide the 550 foot-pounds by the 0.10472 radians per second (engine speed), we get 550/0.10472, which equals 5,252.” Pollak says, explaining the numbers. Of the units, he concludes, “If you multiply torque (in pound-feet) by engine speed (in RPM) and divide the product by 5,252, RPM is converted to “radians per second” and you can get from torque to horsepower and from “pound-feet” to “foot-pounds per second.”
So there you have it: a professional automotive engineer’s explanation on how horsepower can be defined in foot-pounds, but its major component – torque – is measured in pound-feet. The magic for the unit conversions all occurs in how we get that “5,252” number, and you can also see the difficulty with which the units of measure are converted from one to the other.
If you’re talking about torque, be it regarding fasteners or an engine’s output, remember, the “pound-foot” is the correct unit of measure, and the next time the debate comes up, you can either say, “because the SAE says so”, or pull up this article, melt a few brains, and settle it decisively.